Thompson wrote: Went looking for the podcast of this...

Some BBC programmes are issued as podcasts, some are not - the essential difference as far as the BBC is concerned is that you can download and keep podcasts. Some podcasts are edited versions of programmes, and some can be longer than the broadcast edition.

They usually, in my experience, don't make podcasts of programmes with music in them, because they don't have sufficient rights to the music. Sometimes they do - but fade or remove the music.

For example, Inside Science is available as a podcast: on its programme page you will see a Download button (in the UK, anyway):
Inside Science

Morgurgo's programme lacks the download button. It will have a 'Listen Now' button (in the UK, anyway) for as long as they make it available (one month?):
Michael Morpurgo - 10,000 miles